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Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

There exists a mysterious algebraic structure in 8-dimensional space that does not behave in the same way as the ordinary arithmetic that we all learn as children. Somewhat surprisingly, this strange algebra, called the octonions, shows up naturally in the study of certain higher dimensional geometric spaces, called manifolds, that are of importance in physics and in the study of the equations introduced by Einstein in general relativity. Geometers have been studying such spaces for a number of years, mostly using tools from calculus and differential equations. The proposed workshops intends to introduce these researchers to experts in the special octonion algebra, as well as in related special algebraic structures called spinors, to facilitate a cross-pollination of ideas, methods, and techniques. Some of these groups have never before been brought together in this way.

CRM / Université de Montréal

This workshop focuses on several themes related to the fundamental groups of 3-manifolds. The themes include: the theory character varieties, Thurston norm polytopes and fibrations, orderability, profinite rigidity, and variations on the Cannon conjecture. The first week of the workshop will feature mini-courses by Ian Biringer (Boston College), Michelle Chu (Minnesota), Nathan Dunfield (Illinois-Urbana), and Daniel Groves (Illinois-Chicago). The second week will be devoted to research talks.

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

This workshop will focus on geometry, topology and their applications to control systems. Control theory deals with the problem of shaping the behavior of "systems", which can mean an engineered object, such as a robotic arm used for remote surgery, or a natural one, such as a flock of birds or even the brain. The basic driving questions are how to control or design a system which performs as desired. Geometric and topological ideas have led to technological breakthroughs throughout the years, but geometric thinking in engineering has not yet permeated the mainstream. The goal of this workshop is to bring together a diverse group of engineers and scientists working in geometry, topology and their intersection, in order to open new frontiers of research and applications.

CRM / Université de Montréal

The mini-courses and research talks will address several themes, including: nonpositively-curved cube complexes, median spaces, (coarsely) Helly spaces and groups, and various combinatorial notions of nonpositive curvature. The first week of the workshop involves mini-courses by Elia Fioravanti (MPI Bonn), Thomas Haettel (Université de Montpellier), Nima Hoda (ENS Paris), Nir Lazarovich (Technion). The second week will be devoted to research talks.

Group Theory,    Graph Theory and Combinatorics

Centre de recherches mathématiques (CRM)

The mini-courses and research talks will address several themes, including: nonpositively-curved cube complexes, median spaces, (coarsely) Helly spaces and groups, and various combinatorial notions of nonpositive curvature. The first week of the workshop involves mini-courses by Elia Fioravanti (MPI Bonn), Thomas Haettel (Université de Montpellier), Nima Hoda (ENS Paris), Nir Lazarovich (Technion). The second week will be devoted to research talks.

Courses and Events for Math Students and Early Career Researchers,    Graph Theory and Combinatorics

Banff International Research Station (BIRS) / UBCO

Geometry is all around us. The circles and triangles of the Ancient Greeks have never left us. Film, art, and architecture ha ve all been touched by mathematics and geometry. 3D printing, robotics, and origami are a new wave of geometry. At Geometry: Education, Art, and Research, leading researchers pair up with educations and artists to push the boundaries of contemporary geometry.

History and Philosophy of Science and Technology,    Public Lectures and Outreach

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

The workshop is concerned with geometric objects arising from polynomial equations known as algebraic curves. Such curves have been studied extensively since the 19th century, but recent developments in combinatorics have led to a plethora of new techniques and solutions to major problems in the field. Bringing together experts from classical algebraic geometry and the adjacent combinatorial areas, the workshop aims to bridge the different points of views, identify key open problems in the field, and to examine how progress can be achieved via a combination of old and new tools.

Calculus, Differential Equations and Integration,    Graph Theory and Combinatorics

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

The Banff International Research Station will host a diverse, international group of mathematicians in 2023 to study geometric approaches to fluids and optimal transport. The ideas of geodesic settings for fluids have been circulating since the late 1960s, but received a strong surge lately, in the last 5-10 years, with the development of new techniques in infinite-dimensional geometry and group theory. The original idea is that the particles in an ideal liquid or gas move in a curved infinite-dimensional space, in the same way as an airplane flying around the earth: along the shortest path. Properties of the fluid, such as how well it can be predicted in the future, how well it mixes together, and how extreme the speed can be, can all be related to how curved this infinite-dimensional space is, which helps us understand features of the weather and climate geometrically. More recently similar ideas have been used to understand solids as well, for example when a pile of rocks are transported from one place to another at the optimal cost.

Condensed Matter Physics and Materials,    Thermodynamics, Fluid Dynamics and Statistical Physics

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Many important questions in convex geometry are related to the study of sections and projections of convex bodies. For example, can convex bodies be uniquely determined by the size of their sections or projections? What are the largest and smallest sections of the cube? Do convex bodies with smaller sections have smaller volume? A common feature of all these problems is that they are solved with the help of harmonic analysis. The aim of the proposed workshop is to bring together leading experts and young researchers to discuss recent progress in applications of harmonic analysis to convex geometry.

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

The concept of manifold in mathematics corresponds approximately to the everyday idea of a smooth surface --- think of soap bubbles or sheets of fabric --- except that it can have any number of dimensions. A question that lies at the origin of topology, the mathematics of shape, is: can we write down a list of all manifolds? At first, such a classification was attempted through numerical invariants. Over time, the focus of algebraic topology has shifted from using numerical invariants to the algebraic objects underlying them, and then ascended further to studying moduli spaces. This workshop concerns recent breakthroughs in this philosophy for studying of manifolds, combining higher-algebraic methods with novel geometric techniques.

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

Fields Institute

This conference will bring together communities working on two-dimensional Conformal Field Theory (CFT) from different perspectives, some of which have had only limited interactions so far. We are thinking here specifically of the communities working on the probabilistic approach to CFT, the algebraic & geometric approach to CFT, the operator algebraic approach to CFT, and the theoretical physics approach to 2d CFT.

High Energy Physics, Particles and Fields,    Mathematical Physics

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Courses and Events for Math Students and Early Career Researchers,    Algebra

Centre de recherches mathématiques (CRM)

Centre de recherches mathématiques (CRM)

Centre de recherches mathématiques (CRM)

Centre de recherches mathématiques, Université de Montréal

This school intends to present various developments in Riemannian and Kähler geometry around the notion of curvature seen as a tool to describe and understand the geometry of the objects. Each week of the session will have a different flavor, but similar problems and methods will be emphasized, and we expect this will lead to fruitful interactions. Our main target audience is young mathematicians, particularly graduate students and early-career researchers. We expect the school to give them the opportunity to learn key ideas and techniques of the field, with an emphasis on solidifying foundations in view of potential future research. Consequently, junior women mathematicians and those from under-represented minority groups will be given priority for financial assistance. We aim for 100 participants including at least 60 young researchers (PhD students, postdoc fellows). Moreover, the school will also feature problem sessions provided by lecturers and selected talks by young researchers.

Centre de recherches mathématiques (CRM)

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Courses and Events for Math Students and Early Career Researchers,    Numerical Analysis and Computational Mathematics

Centre de recherches mathématiques (CRM)

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Courses and Events for Math Students and Early Career Researchers,    Graph Theory and Combinatorics

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Courses and Events for Math Students and Early Career Researchers,    Graph Theory and Combinatorics

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Courses and Events for Math Students and Early Career Researchers,    Probability and Statistics, Game Theory

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Courses and Events for Math Students and Early Career Researchers,    Systems Biology and Computational Biology

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery